Blender Select Random Face But Not Sides
You can do this in two steps:


Select one of the triangular faces, press ShiftG (Select Similar) and choose Polygon Sides. Now all triangular faces should be selected.
Press space, type in Select Random and hit Enter. Now here comes the trick: You can switch from Select to Deselect mode in the Tool Shelf on the left hand side of the 3D viewport:



If the Tool Shelf is not shown press T while your cursor is in the 3D Viewport.